Not only that, Rust is memory safe ;) As you said I encourage everyone to start using Firefox Nightly (currently 58) on both mobile and desktop as it has the most fresh code and is very stable in my experience (only had issues with it once so far, and I helped them by reporting the bug which got fixed -- I also recommend enabling telemetry in it as it helps them study regressions)

But it's only the CSS style system (Stylo) that is Rust for now, plus some other things, (quoting Manishearth)

The mp4 metadata parser. This has been shipping for a while now, and was the first shipped Rust code.

The URL parser (rust-url). This is not shipping, because it's incomplete and there are some mismatches to deal with. But it exists.

Stylo: Servo's CSS engine in Firefox. By far the biggest one, this is shipping in beta and nightly, and should be there in the 57 release for everything but Android

webrender: Servo's GPU-focused renderer. Not shipping, can be flipped on in nightly. Still has work to be done

encoding-rs: All encoding operations go through this now. Shipping

The U2F stuff: A lot of the U2F code is in Rust. Shipping in nightly though I think it's still off by default (but that will change soon?)

Hope in the future we can see a JS engine that is written entirely in Rust, it would completely blow off the competition.